Respuesta :
ANSWER
It will take 10.71 years for the frogs to grow from 100 to 1000
STEP-BY-STEP EXPLANATION:
Given information
The initial population of the frogs = 100
Percentage increase = 24%
The final population of the growth = 1000 frogs
time =?
Step 1: Write the general formula for calculating the size of a population
[tex]P=P_O(1+r)^t[/tex]Where
P = Final population
Po = initial population
r = rate
t = time
Step 2= convert the growth rate from percentage to decimal
[tex]\begin{gathered} r\text{ = 24 \%} \\ r\text{ = }\frac{24}{100} \\ r\text{ = 0.24} \end{gathered}[/tex]Step 3: Substitute the given data into the above formula and solve for t
[tex]\begin{gathered} 1000=100(1+0.24)^t \\ \text{Divide both sides by 100} \\ \frac{1000}{100}\text{ = }\frac{100}{100}(1+0.24)^t \\ 10=(1+0.24)^t \\ 10=(^{}1.24)^t \\ \text{Take the logarithms of both sides} \\ \text{log 10 = t log(1.24)} \\ 1\text{ = t }\times\text{ 0.0934} \\ 1\text{ = 0.0934t} \\ \text{Divide both sides by 0.0934} \\ \frac{1}{0.0934}\text{ = }\frac{\cancel{0.0934}t}{\cancel{0.0934}} \\ t\text{ = 10.71 years} \end{gathered}[/tex]Hence, it will take 10.71 years for the frogs to grow from 100 to 1000
